題組內容

6. Suppose that three random variables $X_1, X_2$ and $X_3$ are jointly distributed with the following p.d.f. $$f(x_1, x_2, x_3) = 8e^{-2x_1 - kx_2 - x_3}$$ for $x_1 > 0$, $x_2 > 0$, and $x_3 > 0$. Determine (2% for (a), and 6% for (b)-(e), totally 26%)

(a) the value of the constant k;